Let
Find the area between the graphs of and
on the interval
.
First, we draw the graph, shading the region between the two graphs in blue.
For this exercise, since and
cross in the interval we are interested in (and we are calculating the area between the graphs, so we’re really looking at the integral of
) we split the integral into two pieces (at the point the functions cross). We have
on
and
on
; thus, we have
Took me two days staring at my answer of 1/3*(8-4*sqrt2) to realise I made a simple sign error subtracting the final 2/3 instead of adding it. If anyone wants to know how my 2023 began.